Q7 of 50 Page 26

Prove that the arithmetic sequence with first term 1/3 and common difference 1/6 contains all natural numbers.

For the sequence,

a =


d =


an = a + (n-1) × d


Let p be any natural number


p = + (n-1) ×


= +


=


6p = n + 1


Thus, for every natural number p, a value of n exists.


Hence, this arithmetic sequence contains all natural numbers.


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The 8th term of an arithmetic sequence is 12 and its 12th term is 8. What is the algebraic expression for this sequence?

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The Bird problem in Class 8 (The lesson, Equations) can be slightly changed as follows.

One bird said:


“We and we again, together with half of us and half of that, and one more is a natural number”


Write the possible number of birds in order. For each of these, write the sum told by the bird also.


Find the algebraic expression for these two sequences.

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Prove that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers, but no even number.

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Prove that the squares of all the terms of the arithmetic sequence 4, 7, 10, … belong to the sequence.